Froude Number

F r = \frac{V}{g y} (F r = 1 critical)

Fr is the ratio of inertial to gravity wave speed √(gy) in a rectangular (or wide) channel. Fr < 1 subcritical (tranquil), Fr = 1 critical, Fr > 1 supercritical (rapid). A hydraulic jump dissipates energy from supercritical to subcritical.

$F r$: Froude number
$V$ (m/s): Mean velocity
$y$ (m): Hydraulic depth A/T
$g$ (m/s²): Gravity

Step-by-step solved example

V = 1.80 m/s, y = 0.90 m. Classify the flow (g = 9.81).

Fr = V/√(gy). Critical at Fr = 1; jump from super- to subcritical.

1. Wave celerity
√(gy) = √(9.81×0.90) = √8.829 = 2.97 m/s.
2. Froude
Fr = 1.80/2.97 = 0.606 < 1 → subcritical.
$F r = 0.606$

Answer: Fr = 0.61 (subcritical)

10 practice questions

0/10 correct

1.Fr = 1 means the flow is

2.Fr < 1 is

3.A hydraulic jump takes flow from

4.Critical velocity in 1.00 m of water (g = 9.81) is nearest

5.In a non-rectangular channel use hydraulic depth

6.V = 4.0 m/s, y = 0.50 m. Fr is nearest

7.Downstream of a sluice gate the jet is typically

8.Wide-rectangle critical depth yc =

9.Gravity waves cannot propagate upstream when

10.Doubling V at fixed y will